A variant of super-Halley method with accelerated fourth-order convergence

摘要

In this paper, we present a new variant of super-Halley method for solving non-linear equations. Analysis of convergence shows that the method has the order of convergence four. Per iteration the new method requires the same evaluations of the function, the first derivative and second derivative as its classical predecessor, super-Halley method. Numerical results show that the method has definite practical utility.